Update to my question above: I just read, in answer to another thread, "click on the menu item "Enable Automatic Removal""

I am guessing my problem is I have not clicked on that. The Cookie icon is black. When I click on it, I do not see that choice, either in the dropdown list or in Preferences. In the dropdown list, there is "Clean Now". That sounds like a manual way to clear cookies?

As there has not yet been a reply, I am editing this post to reflect my current situation. I hope that's okay.

I have downloaded the Try It version of Cookie5 ver 5.6.2 onto my iMac Retina with OS 10.12.6 and Safari 11.0. In Cookie's window labeled "Removal - Websites," "Safari" appears with a list of websites I have visited. Those whose cookies I want to retain ("favorites") I have checked. The others are unchecked. I clicked on "Use Advanced View" and that "revealed" Enable/Pause Automatic Removal in the menubar icon's dropdown menu. It is enabled. In that same dropdown menu is "Show Cookie" which again displays my list of "favorites" and, on restarting Safari, shows "non-favorites" as having been deleted from that list.

Also, at Cookies Preferences>Advanced>OpenSetupWindow>SelectUnwantedData, I have checked "Non-Favorites" and "History", and at SetRemovalOptions, I have checked "When a browser is quit".

After quitting Safari, Safari Preferences>Privacy>ManageWebsiteData, some "non-favorites" continue to display. And at Safari>History, the history still displays. That is, if Cookie deleted them when I quit Safari, that is not being shown at Safari itself.

In another thread there was a comment about being sure settings for removal are active" in Opera? Are there such settings in Safari? If so, how are they made active?

Or has the installation of Cookie simply made Safari's own display of History and Safari's display at ManageWebsiteData simply OBE?

I have attached a PDF file showing my Cookie settings.

Thank you.